GB-R: A Fast and Effective Gray-Box Reconstruction of Cascade Time-Series

Given some (but not all) monthly totals of people with measles (or counts of product-units sold, or counts of retweets), how can we recover the weekly counts? Requiring smoothness between successive weeks is reasonable - but can we do better, if we have some domain knowledge? For example, we know that measles (flu, count-of-retweets, etc) follow a specific cascade model, like the so-called 'SIS'. The answer is 'yes'. With our proposed GB-R we show how to inject domain knowledge, creating a gray-box model; we show how to set up and efficiently solve the appropriate optimization problem. The desirable properties of our GB-R are: (a) effectiveness, outperforming the best competitors on real, epidemiology data, often by 3x - 25x in reconstruction error; (b) scalability, being linear on the sequence length and (c) interpretability, accurately estimating the parameters of the gray-box model.